A New York City police detective and two Health Department lab technicians who were involved in the investigation of the NBC anthrax scare have tested positive for exposure to anthrax, Mayor Rudolph W. Giuliani announced yesterday. The findings led the city to alter how it responds to incidents that could involve such exposure.

The mayor, at an early afternoon news conference, was quick to say that neither the officer nor the technicians, whom he did not identify, were suffering from the flulike symptoms or skin rashes that characterize anthrax. Instead, he said, initial tests detected a very minute amount of anthrax spores in their nasal passages or on their skin.

Health Commissioner Neal L. Cohen said that the exposure presented ''zero risk'' to the three and that they had been given antibiotics as a precaution.

But the new exposure cases highlighted what city and federal officials have said were flaws in their initial response to the city's first confirmed bioterrorism case, which centered on two letters sent to NBC in September. One, from Trenton, was postmarked Sept. 18; the other, from St. Petersburg, Fla., Sept. 20.

The missteps listed by government officials touched a number of agencies: on Friday, a police detective who responded to the NBC office improperly handled the Trenton letter, which contained a brown sandlike substance later found to include anthrax spores; protective gear worn by the lab technicians testing the letter was not secure enough to prevent exposure; and Health Department and federal law enforcement officials were too slow to tell the mayor's office and the New York Police Department of the potential threat at NBC.

''What we're going to do is as we learn these things, we're going to move forward, recreate our procedures, do things differently,'' Mr. Giuliani said as he was flanked by Dr. Cohen, Police Commissioner Bernard B. Kerik and Richard Sheirer, the director of the city's Office of Emergency Management. ''It's like three weeks ago if I got an envelope like this I would have passed it around to seven or eight people or 10 people. I wouldn't have known the difference. Now you know that you shouldn't.'' All the city officials expressed relief that despite more than 100 additional reports of possible biohazard incidents over the weekend, none were substantiated. Also, all four or five people exposed to anthrax or infected with it as part of the NBC case are expected to recover fully. Health Department officials objected to any suggestion that they did not notify the mayor's office about the NBC case quickly enough.

The inquiry into the origin of the contaminated letter sent to NBC from Trenton accelerated yesterday, with federal and local investigators trying to narrow the list of post offices it could have passed through and starting to examine videotapes from those offices in the hope that the sender did not use a mailbox.

The letter, which arrived at the NBC Nightly News office between Sept. 19 and Sept. 25, bore no return address. Yesterday, details of what happened between the letter's arrival at NBC and its retrieval on Friday by the F.B.I. and city police became clearer, based on interviews with officials at NBC, the mayor's office and the Health Department.

The NBC News staff member who received and opened the letter, and who has not been identified, swept most of the granular material into a trash can and placed the letter into a pile or file where hate mail received by the Nightly News's staff is routinely collected.

Not until Sept. 25, when the letter from St. Petersburg arrived bearing a white powdery substance, did NBC officials call the F.B.I. Federal investigators arrived the next day to collect it, but were not told about the Trenton letter.

City officials did not learn about either letter until Oct. 1, when a doctor who had been visited that same day by Erin M. O'Connor, an assistant to the NBC news anchor Tom Brokaw, called the Health Department to say that he suspected Ms. O'Connor was suffering from anthrax. The doctor also told the Health Department that Ms. O'Connor had handled the St. Petersburg letter and that it had been given to the F.B.I. Investigators say they believe that Ms. O'Connor also handled the Trenton letter, but do not know when.

The department got the letter from the F.B.I and within two days completed tests that showed no evidence of anthrax. Thus, city health officials said, they decided not to notify the mayor's office.

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Last Tuesday, Ms. O'Connor, concerned that she had developed a dark sore on her chest, visited another doctor who took a skin biopsy, and with the Health Department's knowledge, sent the tissue sample to federal health officials for testing.

Coincidentally, about the same time, the NBC employee who had originally opened the Trenton letter remembered that she had put it aside and decided to alert NBC security. Company security sealed the Trenton letter in an envelope or plastic bag and moved it from the third floor to a security office elsewhere at 30 Rockefeller Plaza.

Last Friday, when Ms. O'Connor's skin sample tested positive for anthrax, the city police and F.B.I. were sent to NBC, where they first learned about the Trenton letter.

The unidentified NBC aide who opened the Trenton letter later developed symptoms including a rash and fever, but infection with anthrax has not been confirmed, health officials said yesterday.

A city detective at the NBC office, who was not wearing gloves or other protective gear, opened the envelope or plastic bag and examined the letter. As he did so, he was apparently exposed to a small amount of anthrax. The letter was taken to a Health Department laboratory, where the two technicians quickly determined the presence of anthrax.

Although the technicians were wearing gowns, masks and gloves, they, too, were exposed to the bacilli. Yesterday, Dr. John Kornblum, chief of the Health Department's molecular testing laboratory, said that their masks may not have been properly secured, or perhaps there were gaps in their gowns. ''If you're smiling, maybe there's a little crease'' in the face mask, he said.

City officials said yesterday that a variety of steps would be taken to avoid similar mistakes. ''In hindsight,'' one police official said, ''no one is going to disagree that there should have been more precautions.''

Beginning immediately, a firefighter specially trained in hazardous materials and two police officers -- all equipped with masks and gloves -- will respond to initial, seemingly minor reports of possible biological or chemical threats.

Staff members who handle material brought to the Health Department for anthrax testing will work with the material only after it is placed in a sealed glove box, or they must wear protective gear that completely covers their face and shoulders. ''We don't want to go to the space suits because it's just a little too cumbersome to work in the laboratory and it's a little too impractical,'' Dr. Kornblum said.

The Health Department will also notify the mayor's office of any possibly credible biohazard case, even one that has not been confirmed, said Mr. Sheirer, the director of the Office of Emergency Management. And officials said the F.B.I. had recommitted to immediately telling the Police Department, as it is routinely supposed to do, of any report of a possible biohazard case. ''Even if it is nothing, we would rather know about it,'' Mr. Sheirer said yesterday.

NBC officials said they were not sure when they would be able to reoccupy the Nightly News offices or broadcast again from the regular studio.

As he has done for a month now, Mr. Giuliani urged New Yorkers to live their lives normally and not be intimidated by terrorists.